Alternating currents revision notes · A-Level Physics 9702

Alternating currents

A-Level Physics 9702 · Topic 21 revision notes · A2

Sinusoidal alternating currents described by period, frequency, peak and r.m.s. values, then rectified with diodes and smoothed with a capacitor.

9 definitions to learn word for word, 6 equations in their own column, 5 diagrams and graphs. Read it, cover it, test yourself.

Definitions (mark-scheme wording)EquationsExam traps

21.1Characteristics of alternating currents

Alternating current: a current that changes direction periodically (repeatedly reverses).
Period (T): the time taken for one complete cycle of the alternating current or voltage.
Frequency (f): the number of complete cycles per unit time.
Peak value (I₀, V₀): the maximum value of the current or voltage (measured from zero).
Root-mean-square (r.m.s.) value: the value of the steady direct current (or voltage) that would produce the same mean power in a resistor as the alternating current (or voltage).

A sinusoidal a.c. is written x = x₀ sin ωt, with ω = 2πf.
Power in a resistor P = I²R is always positive and varies at twice the supply frequency.
Mean of sin² over a cycle = ½, so mean power = ½ peak power (resistive load).
For a sinusoid, I_rms = I₀/√2 ≈ 0.71 I₀; the mean current over a cycle is zero.
Peak-to-peak value = 2 × peak value; read peaks from the centre line on an oscilloscope trace.
Oscilloscope: T from time-base × divisions per cycle; V₀ from Y-gain × divisions.
Mains 230 V is the r.m.s. value (peak ≈ 325 V).

Sinusoidal current: peak I₀, period T, and the r.m.s. level at 0.71 I₀.

Power in a resistor: always positive, frequency 2f; the mean is half the peak power.

Use r.m.s. values for power; the peak matters for insulation and breakdown. 230 V mains peaks at 230 × √2 ≈ 325 V.
I_rms = I₀/√2 holds only for sinusoidal waveforms (a square wave has I_rms = I₀).
Mean power is ½I₀V₀, not I₀V₀/√2.

21.2Rectification and smoothing

Rectification: the conversion of an alternating current (or voltage) into a direct current (or voltage), one that flows in one direction only.
Half-wave rectification: rectification in which only one half of each cycle is passed; the other half is blocked (one diode).
Full-wave rectification: rectification in which both halves of each cycle give output in the same direction (bridge of four diodes).
Smoothing: reducing the variation (ripple) of a rectified output, using a capacitor in parallel with the load.

A diode conducts in one direction only (arrow = direction of conventional current).
Half-wave: one diode in series with the load; output is zero for half of each cycle.
Full-wave: bridge rectifier; two diodes conduct in each half-cycle, current through the load always in the same direction.
Smoothing capacitor charges to the peak, then discharges through the load between peaks, holding the p.d. up.
Ripple is smaller when the time constant RC is large compared with the time between peaks.
Larger C (or larger load R) gives smoother output; a smaller load resistance gives more ripple.
Full-wave output has ripple at 2f, so it smooths more easily than half-wave.

Half-wave rectification: the input (dashed) and the output (solid), which is zero during the negative half-cycles.

Bridge rectifier: whichever input is positive, current leaves at + and returns at -, always the same way through the load R.

Full-wave output (humps) smoothed by a capacitor: it charges at each peak and discharges through R between them, leaving a small ripple.

Full-wave rectified 50 Hz a.c. has ripple at 100 Hz: both half-cycles give a hump.
The smoothing capacitor goes in parallel with the load, not in series.
More smoothing needs a larger time constant (bigger C or bigger R), not a smaller one.